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Efficient Placement and Dispatch Efficient Placement and Dispatch of Sensors in a Wireless Sensor of Sensors in a Wireless Sensor NetworkNetwork

Prof. Yu-Chee TsengProf. Yu-Chee Tseng

Department of Computer ScienceDepartment of Computer ScienceNational Chiao-Tung University National Chiao-Tung University

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Outline Introduction Sensor Placement Sensor Dispatch Conclusions

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Introduction Wireless sensor networks (WSN)

Tiny, low-power devices Sensing units, transceiver, actuators, and even

mobilizers Gather and process environmental information

WSN applications Surveillance Biological detection Monitoring

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Introduction Sensor deployment is a critical issue because

it affects the cost and detection capability of a wireless sensor network

A good sensor deployment should consider both coverage and connectivity

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Coverage Connectivity

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Review The art gallery problem (AGP) asks how to use a

minimum set of guards in a polygon such that every point of the polygon is watched by at least one guard.

However, the results cannot be directly applied to sensor deployment problem because AGP typically assumes that a guard can watch a point as

long as line-of-sight exists Sensing distance of a sensor is normally finite

AGP does NOT address the communication issue between guards Sensor deployment needs to address the connectivity issue

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Two Issues in Sensor Deployment Sensor placement problem:

Ask how to place the least number of sensors in a field to achieve desired coverage and connectivity properties.

Sensor dispatch problem: Assume that sensors are mobilized Given a set of mobile sensors and an area of interest II

inside the sensing field AA, to choose a subset of sensors to be delegated to II with certain objective functions such that the coverage and connectivity properties can be satisfied

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Outline Introduction Sensor Placement Sensor Dispatch Conclusions

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Sensor Placement Problem Input: sensing field AA

AA is modeled as an arbitrary-shaped polygon AA may contain several obstacles

Obstacles are also modeled by polygons Obstacles do NOT partition AA

Each sensor has a sensing distance rs and communication distance rc

But we do NOT restrict the relationship between rs and rc

Our goal is to place sensors in AA to ensure both sensing coverage and network connectivity using as few sensors as possible

Obstacle

Obstacle

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Two Intuitive Placements

rc

rs

3rs

Consider coverage first Consider connectivity first

Need to add extra sensorsto maintain connectivity when 3c sr r

Need to add extra sensorsto maintain coverage when 3c sr r

rs

3rs

3rs 3rsrc

3rs

rc rc

rc rc

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Proposed Placement Algorithm Partition the sensing field AA into two types of sub-re

gions: Single-row regionsSingle-row regions

A belt-like area between obstacles whose width is NOT larger than , where rmin= min(rs, rc)

We can deploy a sequence of sensors to satisfy both coverage and connectivity

Multi-row regionsMulti-row regions We need multi-rows sensors to cover such areas Note: Obstacles may exist in such regions.

min3r

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Step 1: Partition the Sensing Field From the sensing field AA, we identify all single-row regions

Expand the perimeters of obstacles outwardly and AA’s’s boundaries inwardly by a distance of rmin

If the expansion overlaps with other obstacles, then we can take a projection to obtain single-row regions

The remaining regions are multi-row regions.

3rmin

Expansions

Obstacle

Obstacle

Obstacle

3rmin

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An Example of Partition

Obstacle

Obstacle

min3r

Obstacle

2

7Obstacle

1

3

4 5

6

Obstacle

12

4 56

3Multi-row regions

Single-row regions

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Step 2: Place Sensors in a Single-row Region Deploy sensors along the bisector of region

< 3rminwidth

Obstacle

Obstacle

Obstacle

Obstacle

< 3rminwidth+ +

+ ++ +

+

Case

(a)

(b)

Small Regions Bisectors Sensor Deployment

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+

+

+

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Step 3: Place Sensors in a Multi-row Region We first consider a 2D plane without boundaries & o

bstacles Deploy sensors row by row A row of sensors needs to guarantee coverage and connec

tivity Adjacent rows need to guarantee continuous coverage

Case 1: Sensors on each row are separated by rc Adjacent rows are separated by

Case 2: Each sensor is separated by

3c sr r

3c sr r

224cr

s sr r

3 sr

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Case 1: 3c sr r

rs

rs

rc

rs rs -2 rc2

4

rc2

rs

rs/rc

rs23

rs2

rs

rs

rs

rc

rs -2 rc2

4

rs

rc2

rs > rc rs = rc rs < rc < 3rs

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Case 2: 3c sr r

rs23

rs

rc rs

rs

rs2

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Refined Step 3: For a multi-row region with boundaries and

obstacles, We can place sensors one by one according to the

following locations (if it is not inside an obstacle or outside the region)

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Step 4:

Obstacle

uncovered areas

connectivity

Obstacle

Three unsolved problems Some areas near the boundaries

are uncovered Need extra sensors between

adjacent rows to maintain connectivity when

Connectivity to neighboring regions needs to be maintained

3c sr r

Solutions Sequentially place sensors along

the boundaries of the regions and obstacles

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Simulation Results Sensing fields

(a) Rectangle (b) Circle (c) Non-convex polygon

(d) H-shape (e) Office 1 (f) Office 2

40

75

89

41

1987

37

57 40

35

4828

75

89

6 4

4

3

28

3

12

17 28

49

20

75

89

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Simulation Parameters We use (rs, rc) = (7,5), (5,5), (3.5,5), (2,5) to re

flect the four cases Comparison metric

Average number of sensors used to deploy Compare with two deployment methods

rs

3rs

3rs 3rs

rc

rc

Coverage-first Connectivity-first

, , 3 , 3s c s c s c s s cr r r r r r r r r

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Simulations (rs vs. rc)

227268

341267

315

500

360 361 386

0

100

200

300

400

500

600

700

800

Num

ber

of D

eplo

yed

Sens

ors Ours

Cov.-firstConn.-first

217254

323

253298

470

341341363

0

100

200

300

400

500

600

700

Num

ber

of D

eplo

yed

Sens

ors Ours

Cov.-firstConn.-first

141171

225

174210

353

252 253 265

0

100

200

300

400

500

Num

ber

of D

eplo

yed

Sens

ors Ours

Cov.-first

Conn.-first

126159

220

169206

367

273 273 273

0

100

200

300

400

500

Num

ber

of D

eplo

yed

Sens

ors Ours

Cov.-first

Conn.-first

148193

275

201253

470

328 340328

0

100

200

300

400

500

600

Num

ber

of D

eplo

yed

Sen

sors Ours

Cov.-firstConn.-first

(a) Rectangle (b) Circle

(d) H-shape (e) Office 1 (f) Office 2

rs > rc rs = rc rs < rc < 3rs rs > rc rs = rc rs < rc < 3rs

rs > rc rs = rc rs < rc < 3rs rs > rc rs = rc rs < rc < 3rs rs > rc rs = rc rs < rc < 3rs

111135

178142

168

284

215 215 215

0

100

200

300

400

500

Num

ber

of D

eplo

yed

Sens

ors Ours

Cov.-first

Conn.-first

(c) Non-convex polygon

rs > rc rs = rc rs < rc < 3rs

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Simulations (Shapes of A)

738

556428

553

744 786

962

717

907

1168 12351281

0

200

400

600

800

1000

1200

1400

Rectangle Circle Non-convex

H-shape Office 1 Office 2

Num

ber

of D

eplo

yed

Sen

sors

Ours

Conn.-first

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Outline Introduction Sensor Placement Sensor Dispatch Conclusions

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Problem Definition We are given

A sensing field AA An area of interest II inside AA A set of mobile sensors SS resident in AA

The sensor dispatch problem asks how to find a subset of sensors S’S’ in SS to be moved to II such that after the deployment, II satisfies coverage and connectivity requirements and the movement cost satisfies some objective functions.

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ExampleAA

IIMobile sensor

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ExampleAA

II

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ExampleAA

II

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Two Objective Functions Minimize the total energy consumption to move sens

ors

: unit energy cost to move a sensor in one step di : the distance that sensor i is to be moved

Maximize the average remaining energy of sensors in S’ after the movement

ei : initial energy of sensor i

'

min m ii S

d

'

( )max

| ' |

i m ii S

e d

S

m

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Proposed Dispatch Algorithm (I) Run any sensor placement algorithm on II to get the t

arget locations L={(x1, y1),… ,(xm, ym)} For each sensor , determine the energy cost c(si,

(xj, yj)) to move si to each location (xj, yj))

Construct a weighted complete bipartite graph , such that the weight of each edge is w(si, (xj, yj)) = - c(si, (xj, yj)) , if objective function (1) is us

ed; or as w(si, (xj, yj)) = ei - c(si, (xj, yj)), if objective function (2) is

used

is S

( , ( , )) ( , ( , ))i j j m i j jc s x y d s x y

( , )G S L S L

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Proposed Dispatch Algorithm (II) Construct a new graph from G,

where L is a set of |S|-|L| elements, each called a virtual location. The weights of edges incident to L are set to wmin, where wmin ={min. weight in G}-1.

Find the maximum-weight perfect-matching M on graph G by using the Hungarian method.

For each edge c(si, (xj, yj)) in M such that , move sensor si to location (xj, yj) via the shortest path. If , it means that we do not have sufficient

energy to move all sensors. Then the algorithm terminates.( , ( , )) 0i i j je c s x y

( , )j jx y L^

^^

( , { })G S L L S L L ^ ^^

^

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An Example of Dispatch

II

A

BD

C

E

Initially, there are five mobile sensors A, B, C, D, and E

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An Example of Dispatch

II

A

BD

C

E

Run sensor placement algorithm on II to get the target locations

L={(x1, y1), (x2, y2), (x3, y3), (x4, y4)}1 2

3 4

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An Example of Dispatch

II

A

BD

C

E

1 2

3 4

Compute energy cost (assume =1)m

1 1 2 2

3 3 4 4

1 1 2 2

3 3 4 4

1 1 2 2

3 3 4 4

1

( , ( , )) 9 ( , ( , )) 12

( ,( , )) 8 ( , ( , )) 11

( ,( , )) 11 ( , ( , )) 11

( ,( , )) 9 ( , ( , )) 9

( ,( , )) 10 ( , ( , )) 6

( ,( , )) 11 ( , ( , )) 8

( ,( ,

c A x y c A x y

c A x y c A x y

c B x y c B x y

c B x y c B x y

c C x y c C x y

c C x y c C x y

c D x

1 2 2

3 3 4 4

1 1 2 2

3 3 4 4

)) 14 ( , ( , )) 13

( ,( , )) 12 ( , ( , )) 10

( ,( , )) 33 ( , ( , )) 35

( ,( , )) 30 ( , ( , )) 31

y c D x y

c D x y c D x y

c E x y c E x y

c E x y c E x y

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An Example of Dispatch Construct the weighted complete bipartite graph G and assign weight on each

edge

A

B

C

D

E

1

2

3

4

S L

Weights of edges (assume that all sensors havethe same initial energy 40 & 1st objective function is used)

A B C D E

1 31 29 30 26 7

2 28 29 36 27 5

3 32 31 29 38 10

4 29 31 32 30 9

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An Example of Dispatch Construct the new graph G from G by adding |S|-|L| virtual locations

S L

Weights of edges

A B C D E

1 31 29 30 26 7

2 28 29 34 27 5

3 32 31 29 28 10

4 29 31 32 30 9

5 4 4 4 4 4

^

Virtual location

A

B

C

D

E

1

2

3

4

5

Min.

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An Example of Dispatch Use the Hungarian method to find a maximum-weighted perfect-matching M

S L

Weights of edges

A B C D E

1 31 29 30 26 7

2 28 29 34 27 5

3 32 31 29 28 10

4 29 31 32 30 9

5 4 4 4 4 4

A

B

C

D

E

1

2

3

4

5

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An Example of Dispatch Move sensors to the target locations

S L

A

B

C

D

E

1

2

3

4

5

II

A

BD

C

E

1 2

3 4

Do not move

A

B D

C

II

E

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Find the Shortest Distance d(si, (xj, yj)) Find collision-free shortest path

A sensor is modeled as a circle with a radius r Expand the perimeters of obstacles by the distance of r to find the col

lision-free vertices. Connect all pairs of vertices, as long as the corresponding edges do n

ot cross any obstacle. Using Dijkstra’s algorithm to find the shortest path.

Obstacle 1

si

Obstacle 2

(xj, yj)

r

r Obstacle 3

r

a

b

c

d

e

f

g

h

collision-free vertices

collision-free edges

expanded area

shortest path

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Find the Maximum-Weight Perfect-Matching

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The Hungarian Method

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Time complexity The time complexity of our sensor dispatch

algorithm is O(mnk2 + n3) m: number of target locations in II n: number of mobile sensors k: number of vertices of the polygons of all

obstacles and II

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Simulations

0

2000

4000

6000

8000

10000

12000

14000

20 40 60 80 100 120

Number of Sensors in I

Tot

alE

nerg

yfo

rM

ovem

ent

Ours

Greedy

Random

500

520

540

560

580

600

620

640

660

20 40 60 80 100 120Number of Sensors in I

Ave

rage

Rem

aini

ngE

nerg

yof

Sens

ors

Ours

Greedy

Random

Greedy: sensors select the closest locations Random: sensors randomly select locations

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Conclusions We propose a systematical solution for sensor deplo

yment Sensing field is modeled as an arbitrary polygon with obs

tacles Allow arbitrary relationship between rc and rs

Fewer sensors are required to ensure coverage and connectivity

An optimal-energy dispatch algorithm is presented to move sensors to the target locations under two energy-based objective functions